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Potato paradox
- TN1ck 8y agoAlmost everyone I know could not solve it correctly without a lot of hints. Even when you say: „It is not the answer you first think it is“. I like to use it when someone feels too smart and won’t acknowledge that he might be wrong about something. For example, a friend was arguing that the moon landing didn’t happen because the capsule was too small to hold the needed fuel. I asked him the paradox, he got it wrong. I followed with: „how can you believe to be right about rocket science, when you weren’t able to get this simple question right?“
- evancox100 8y agoAnd how did the conversation go after that?
- el_don_almighty 8y ago"She dumped her drink on my head and walked away."
- SideburnsOfDoom 8y agoDoes it matter a lot? Do you really need to be friends with a moon-landing denier?
- mar77i 8y agoShows how easy it is to reject complicated things if you manage to get so much of the more simple things wrong.
- iDemonix 8y agoI bet you're a blast to be around.
- JumpCrisscross 8y ago> You have 100 lb of potatoes, which are 99 percent water by weight Would this be less of a paradox if we talked about water balloons? Potatoes, in real life, are 80% water [1]. [1] http://umich.edu/~elements/web_mod/potato/fact.htm http://umich.edu/~elements/web_mod/potato/fact.htm
- OskarS 8y agoYou can't really "dry" water balloons. The water in them don't really evaporate.
- douglaswlance 8y agoThe water does really evaporate, just takes a lot longer than potatoes.
- ars 8y agoLettuce is 96%: https://www.myfooddata.com/articles/vegetables-high-in-water.php https://www.myfooddata.com/articles/vegetables-high-in-water... Potatoes are a poor choice, most common salad vegetables are around 95%.
- JackFr 8y agoNot a paradox, but the 80% is the reason that potato chips are made close to the farm. Frito-Lay doesn't want to ship water. http://www.econtalk.org/odonohoe-on-potato-chips-and-salty-snacks/ http://www.econtalk.org/odonohoe-on-potato-chips-and-salty-s... Fascinating podcast about the economics of the (potato) chip industry.
- daemin 8y ago"Potato Paradox" just sounds so much better than "Water Balloon Paradox"
- Bartweiss 8y agoI'll bet using potatoes does makes the the question harder for people. However simple the math, it runs up against the intuition "potatoes are full of starchy solids, I'll bet lowering their water weight one point wouldn't be that noticeable a change". Heck, I'll bet this is made harder by exposure to baked potatoes. The actual study on water loss via baking potatoes is paywalled, sadly, but discussion on some fitness forums says that there's a >5% weight loss from baking - which would constitute a 1-point change in water weight. Still an interesting question, but it feels a bit cheap to invoke a physical intuition that's completely irrelevant.
- pgroves 8y agoReminds me of how bond yields work. If the interest rate guess from 1% to 2% on an existing bond, the bond itself has to lose 50% of its value. I think the potato story is somehow less intuitive.
- techbio 8y agoThe potato paradox disappears entirely with the right illustration [1]. Something similar (though not quite so clear as paradox's grid) for bonds: [2]. [1] https://en.wikipedia.org/wiki/File:Potato_paradox.svg https://en.wikipedia.org/wiki/File:Potato_paradox.svg [2] https://bogleheads.org/w/images/thumb/8/84/Bond_-_Premium_-_Discount_Curve.png/500px-Bond_-_Premium_-_Discount_Curve.png https://bogleheads.org/w/images/thumb/8/84/Bond_-_Premium_-_...
- jacobkg 8y agoThat’s true only if the bond has an “infinite” term. Meaning it pays interest forever but you never get your initial principal back If a bond has say a one-year term then it won’t lose 50% of its value if interest rates double from 1 to 2 percent because you still get your original full investment back after one year. It’s value instead drops by about 1%. For a longer term example, a bond purchased for $1,000 and 1% interest rate with 30 years left is worth $776 if interest rates rise to 2% Source: https://m.free-online-calculator-use.com/bond-value-calculator.html https://m.free-online-calculator-use.com/bond-value-calculat...
- AnimalMuppet 8y agoThat's not how bond yields work. Let's say I have a bond that has a face value of $100, yields 1%, and matures in 1 year. It's value today is $99. Now interest rates go to 2%. That bond is now worth $98, because 1 year from now, at 2% interest, it will be worth $100. But for longer term bonds (30 years, say), what you said can be true.
- tompetry 8y agoThis is true in limited cases. Changes in bond values in relation to interest rate changes is much more involved than this. The first derivative is known as "duration" while the second derivative is known as "convexity". The size and timing of payments will vary from bond to bond, which heavily affects interest rate risk: Duration: https://en.wikipedia.org/wiki/Bond_duration https://en.wikipedia.org/wiki/Bond_duration Convexity: https://en.wikipedia.org/wiki/Bond_convexity https://en.wikipedia.org/wiki/Bond_convexity
- preinheimer 8y agoThe birthday paradox comes up a lot in computing, I wonder if there's more places the potato paradox would apply.
- LanceH 8y agoFirst 90% of the project takes the first 90% of the time/budget and the last 10% of the project takes the other 90%?
- the-dude 8y ago80/20 Pareto Principle
- BlackFly 8y agoPossibly. If you have 99% free users and you want to get to 98% free users by convincing free users to stop using your platform, then you need to lose half of your users. It will come up anytime you have a secondary metric which is a percentage that you want to decrease but the total is the primary metric that people focus on.
- meguest 8y agoCan you explain that? Why would I need to lose 1/2 of my free users? I'm not sure I understand the paradox.
- ballenf 8y agoThe key phrase was by convincing free users to quit, i.e. the number of paying users remains unchanged but you want to improve the ratio of paying to free. To double the ratio, you have to halve the total (being sure that no paying customers quit).
- Stratoscope 8y agoWhat helped me understand this is to look at a specific example. One way to have 99% free users is to have 99 free users and one paid user. Similarly, a way to have 98% free users is to have 98 free users and two paid users. But GP didn't say "convert one free user to paid" or "acquire another paid user by other means." The number of paid users isn't changing: you will still only have one paid user. So you have to cut both numbers in half to keep the same ratio. Instead of 98+2, you end up with 49+1 to have 98% free users.
- apotatopot 8y agodespite my username, I'm going to have to quit coming here if we're going to be a repost trash bin for reddit.
- sp332 8y agoHN has been this for at least 3 years - well before your username was created here. https://hn.algolia.com/?query=Potato%20paradox&sort=byDate&dateRange=all&type=story&storyText=false&prefix&page=0 https://hn.algolia.com/?query=Potato%20paradox&sort=byDate&d...
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- elicash 8y agoWikipedia has a list of paradoxes: https://en.wikipedia.org/wiki/List_of_paradoxes https://en.wikipedia.org/wiki/List_of_paradoxes
- umvi 8y agoI wonder if this is ever used in marketing tactics to disguise the amount of loss
- rplnt 8y agoAnother somewhat similar (in that the result is unintuitive) problem about false positives: Imagine that you have an HIV test that is 95% accurate (false positive rate of 5%). and around 2% of tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive? Is it 95%? Nope, actually just 29%. You do the test again. Numbers from wiki about the paradox: https://en.wikipedia.org/wiki/False_positive_paradox https://en.wikipedia.org/wiki/False_positive_paradox
- nabla9 8y agoSame issue comes up when you discuss effectiveness of ethnic profiling of Muslims/brown skinned people in airports. Sam Harris was unable to wrap his head around this and was sticking to his common sense intuition. Strong profiling is not mathematically optimal for discovering rare malfeasors http://www.pnas.org/content/106/6/1716.full?sid=3bc684ec-b593-41e9-b03e-2e3f32bc42b0 http://www.pnas.org/content/106/6/1716.full?sid=3bc684ec-b59...
- LeifCarrotson 8y agoThe Sam Harris article referenced, for anyone else who was unfamiliar with the controversy: https://samharris.org/in-defense-of-profiling/ https://samharris.org/in-defense-of-profiling/
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- zouhair 8y agoJust wow.
- Bartweiss 8y agoAnd more recently, UK police have discovered that surveilling crowds with facial recognition software produces almost entirely false positives, even if the software is supposedly quite accurate at picking out criminals. Not that they care or plan to stop using it, of course. https://arstechnica.com/tech-policy/2018/05/uk-police-say-92-percent-false-positive-facial-recognition-is-no-big-deal/ https://arstechnica.com/tech-policy/2018/05/uk-police-say-92...
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- mikeyouse 8y agoNot exactly the same, but I stumbled on another seemingly confusing math reality a little while back. It's probably obvious for places that measure their mileage in gallons/100 miles or kms or whatnot, but for MPG: If you could chose to increase the average fuel economy of a car, which of these would save the most fuel: 1. 10mpg -> 12mpg 2. 12mpg -> 15mpg 3. 15mpg -> 20mpg 4. 20mpg -> 30mpg 5. 30mpg -> 60mpg Of course with a little thought, it turns out that they all save the same amount of fuel, but it's hard to wrap my brain around the fuel savings being equal between 10mpg-12mpg and 30mpg-60mpg.
- russdill 8y agoThis relates to another mathematical "oddity". Some regions in the EU measure fuel economy with km/l, while others measure in l/100km. Years ago, when the EU first released fleet fuel economy standards, there was a bit of confusion as some manufacturers averaged the fuel economy of their fleet and then converted to the appropriate units. Which gives a different result than converting to the appropriate units and then averaging.
- russdill 8y agoIncidentally, inverting your mpg figures to gpm actually makes your conundrum much clearer and helps to explain why many countries use the latter. 100 / 10 = 10 100 / 12 = 8⅓ 10 - 8⅓ = 1⅔ 100 / 30 = 3⅓ 100 / 60 = 1⅔ 3⅓ - 1⅔ = 1⅔
- csours 8y agoReformatting parent for readability: 100 / 10 = 10 gallons used 100 / 12 = 8⅓ gallons used 10 - 8⅓ = 1⅔ gallons saved --- 100 / 30 = 3⅓ gallons used 100 / 60 = 1⅔ gallons used 3⅓ - 1⅔ = 1⅔ gallons saved --- As a side note: I worked in the factory that make Chevy Tahoes when they started making 2 mode hybrids. The hybrids didn't make more highway mpg, but they improved city milage from 16 mpg to 20 mpg. One of the problems is that doesn't sound like much of an improvement, but it's actually 1 1/4 gallons saved per 100 miles. https://www.autotrader.com/car-news/chevy-tahoe-hybrid-great-idea-not-good-enough-260370 https://www.autotrader.com/car-news/chevy-tahoe-hybrid-great...
- VikingCoder 8y agoSimpson's Paradox is my favorite: https://en.wikipedia.org/wiki/Simpson%27s_paradox https://en.wikipedia.org/wiki/Simpson%27s_paradox
- Pfhreak 8y agoThis isn't the intuitive result? If one part in 100 of the potatoes is solid, and you want to increase that to 2 parts in 100 that's equivalent to 1 part in 50...
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- mar77i 8y agono, really, it's true, I just tried it: 1 / 100: 0.01 1 / 99: 0.01010101 That's just a bit more than a percent of that percent of change, and not a 100% change, as would be required for a 2:98 ratio.